The 'localization model' of rubber elasticity: comparison with torsional data for natural rubber networks in the dry state

Previously reported results from determinations of the first derivative of the elastic contribution to the free energy density function for dicumyl peroxide crosslinked natural rubber were analysed within the context of the Gaylord-Douglas 'localization model' of rubber elasticity. It was found that the dry state properties of the rubbers are well described by the localization model and that the non-classical contribution to rubber elasticity arising from the confinement of network chains by surrounding chains varies according to the theory. Specifically, a single measure of localization G_e is required to fit the experimental results and the variation of this parameter follows the predictions of the theory, namely, G_e is approximately equal to the rubbery plateau modulus at the limit of zero crosslinking and subsequently follows a linear dependence on crosslink density. The only other parameter in the model, the prefactor to a classical term, was set to the classical phantom value assuming a tetrafunctional network and assuming that each dicumyl peroxide molecule decomposed to form one crosslink.